Here is John Burgess’s amusing description of Quine’s view of mathematical ontology as motivated by the indispensability argument, from “Mathematics and the Bleak House” (Phil. Math. 12, 2004).
Quine…urged a very different sort of reason for accepting the existence of numbers (or other abstract mathematical entities to which numbers could be “reduced”). According to Quine, we must (alas, with the greatest reluctance!) resign ourselves (ah, that it should have come to this!) to accepting (unbidden and unwelcome!) mathematical entities, because (most regrettably and unfortunately!) mention of them seems (would that it were not so!) to be an unavoidable requirement (how cruel a necessity!) in formulating scientific theories.
I, for one, enjoy seeing a reconstruction of Quine’s inner dialogue as he was arguing himself out of his long held nominalism.
A Philosopher's Take 
Posted on March 14, 2015 by Aaron Thomas-Bolduc